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As a molar percentage, 80.3 percent of a boron sample is boron 11 and the remainder is boron 10.
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What is the average molar mass of the boron sample?
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We are told that a sample of boron consists of 80.3 percent boron 11, while the remainder of the sample consists of boron 10.
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Boron 10 and boron 11 are isotopes of boron.
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Isotopes are atoms that have the same number of protons but a different number of neutrons.
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In other words, isotopes are atoms of the same element that have a different mass and a different mass number.
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The mass number is the number written to the top left of the element symbol.
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The mass number is the sum of the number of protons and neutrons in the nucleus.
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This value is not the exact mass of an atom of an isotope.
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However, it is approximately equal to the isotopic mass and unified atomic mass units.
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With this background information in mind, let’s return to the question.
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We want to determine the average molar mass of the boron in the sample.
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When we think about how to calculate a standard average, we might think that we could just sum the isotopic masses, then divide by the total number of isotopes.
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So, in the case of the sample, we would sum together the approximate isotopic masses of each isotope, then divide by two, the total number of isotopes.
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But this type of average does not take into account the fact that boron 11 makes up considerably more of the sample than boron 10.
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So instead of calculating a standard average, we need to calculate a weighted average.
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More specifically, the weighted average we need to calculate is the average atomic mass.
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The average atomic mass is calculated by multiplying the isotopic abundance of one isotope times its isotopic mass, then adding this to the isotopic abundance of the second isotope times its isotopic mass.
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Isotopic abundance is a percentage that represents the relative amount of an isotope.
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So for boron 11, the isotopic abundance is 80.3 percent.
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For this calculation, we’ll use the approximate isotopic mass, which has the same value as the mass number with units of unified atomic mass units.
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The second isotope of boron is boron 10 with an approximate isotopic mass of 10 unified atomic mass units.
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The isotopic abundance or molar percentage of boron 10 was not provided in the question, but it can easily be determined.
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100 percent of the sample contains 80.3 percent boron 11, with the remainder being boron 10.
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This means that the isotopic abundance of boron 10 is 19.7 percent.
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Before we can continue with the calculation, we need to rewrite each percentage in decimal notation.
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We can accomplish this by dividing each percentage by 100 percent.
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Now we can perform the calculations inside of the parentheses, then add together the resulting answers.
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This gives us an average atomic mass of 10.803 unified atomic mass units.
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But the question asked for the average molar mass, not the average atomic mass.
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The average molar mass has the same numerical value as the average atomic mass but has units of grams per mole instead of unified atomic mass units.
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Rounded to one decimal place, we have determined that the average molar mass of the boron sample is 10.8 grams per mole.